What is the Greatest Common Factor of 76000 and 76005?

Greatest common factor (GCF) of 76000 and 76005 is 5.

GCF(76000,76005) = 5

We will now calculate the prime factors of 76000 and 76005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76000 and 76005.

How to find the GCF of 76000 and 76005?

We will first find the prime factorization of 76000 and 76005. After we will calculate the factors of 76000 and 76005 and find the biggest common factor number .

Step-1: Prime Factorization of 76000

Prime factors of 76000 are 2, 5, 19. Prime factorization of 76000 in exponential form is:

76000 = 2⁵ × 5³ × 19¹

Step-2: Prime Factorization of 76005

Prime factors of 76005 are 3, 5, 563. Prime factorization of 76005 in exponential form is:

76005 = 3³ × 5¹ × 563¹

Step-3: Factors of 76000

List of positive integer factors of 76000 that divides 76000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 25, 32, 38, 40, 50, 76, 80, 95, 100, 125, 152, 160, 190, 200, 250, 304, 380, 400, 475, 500, 608, 760, 800, 950, 1000, 1520, 1900, 2000, 2375, 3040, 3800, 4000, 4750, 7600, 9500, 15200, 19000, 38000

Step-4: Factors of 76005

List of positive integer factors of 76005 that divides 76000 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135, 563, 1689, 2815, 5067, 8445, 15201, 25335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76000 and 76005. The biggest common factor number is the GCF number.
So the greatest common factor 76000 and 76005 is 5.

Also check out the Least Common Multiple of 76000 and 76005